THE CASE OF NORWAY (Co-author: Erling Steigum, [r.)
4. SIMULATION RESULTS
This section presents two scenarios. First we report a baseline simulation in which no wealth consumption takes place neither in the short nor the long run. Then we
consider a wealth consumption scenario in which the government's petroleum wealth is consumed in the course of the next forty years, before a new steady state is approached. This leaves future generations with a lower national wealth and higher taxes than in the baseline case. Public expenditures on goods, services and transfers are identical in the two simulations, but taxes are different, see Figure 1.
The wealth consumption scenario illustrates what may happen if the government reduces taxes instead of accumulating other assets to compensate for vanishing petroleum wealth during the next forty years. Such a policy is not unlikely, resulting for example from political pressure from special interest groups. Inour model the tax cuts will boost current consumption at the expense of the consump-tion of future generaconsump-tions.
Inthe baseline simulation, the gross tax rate is not constant over time because of the effects of population ageing and the social security system. During the period from 1988 to 2038 the tax rates increase gradually, and thereafter they decrease marginally. When the baby-boomers start to retire from about 2012,social security transfers will begin to accelerate. This explains much of the baseline tax increases in Figure 1.7
Inthe wealth consumption simulation, taxes are lower than baseline up till 2013.
Sinæ all the government petroleum revenues are used to finance the tax cuts, no part of the petroleum wealth is transformed to other government assets. This implies a total deterioration of public wealth equal to 1134billion 1988 kroner in 2028.In2028 the public wealth consumption stops and taxes are raised in order to stabilize the new lower level of public wealth per effiåency unit of labor, see Figure 2. We assume that the loss of public wealth (per effiåency unit of labor) is permanent, i.e. the wealth consumption growth path approaches a steady state.
After the tax cuts in 1993-2013,tax rates are increased considerably and from 2042 the tax rate is stabilized at a significantly higher level than the baseline tax rate.
7 The problems of financing the social security system in response to popu-lation ageing are adressed in Steigum (1993).
Figure 1
1988 1998 2008 2018 2028 2æ8 2048 2058 2068 2078 2088
Figure 2
- -_- - - Wealth consumption
Net public financial assets incl.petroleum wealth
"'
-,"
-,-,"' "'
-,"
..._---
---1988 1998 2008 2018 2028 2æS 2048 2058 2068 2078 2088
---- Baseline
- - - Wealth consumption
The intergenerational welfare effects of the wealth consumption policy are illu-strated in Figure 3, which shows the changes in per capita consumption of successive generations when each are in age group 40-44 years. Since all gener-ations have identical preferenæs and the real rate of interest is constant, the consumption of a representative consumer in any period is proportional to the present value of his lifetime income. Therefore, consumption in any age group can act as a welfare index, and our choice of age group 40-44 to represent each gener-ation's consumption is arbitrary. Figure 3 shows that the .generations who get tax cuts in 1993-2013 without being seriously hurt by the tax increases later, are those who benefit from the wealth consumption policy. In particular this is the case for those of age 40-44 years in the first periods. Young generations gain little and all generations younger than 10 years in 1988-92 (40 years in 2018-2022, see Figure 3) loose because of the future tax increases. Observe that the results also reflect that younger generations will receive larger bequests from older generations that gained from the policy.
In steady state, the consumption of all generations drops by 14 percent compared to the baseline simulation. Figure 3 reveals a remarkable lack of symmetry be-tween the consumption gains of the winners and the consumption loss of the very young (and unborn) generations. This is because the real rate of interest is much greater than the natural rate of growth, generating substantial compounded interest effects over lang time spans.
Figure 4 highlights the effects of the wealth consumption policy on aggregate private wealth. First, the tax cuts lead to increased accumulation of private wealth, because the generations who gain wish to save more in order to smooth consump-tion over time and leave larger bequests. Expectaconsump-tions of increased future taxes add to this effect on private saving. In the longer run, private wealth declines below the baseline wealth because lower welfare reduces life cycle savings and bequests.
Figure 5 illustrates the effect of the policy on the stock of foreign assets (incl. the 100
Figure 3 Changes in consumption per capita relative to baseline, age group
4D-44 years
-4,000/0 4,00%
-8,00%
-12,00%
-16,00%
1988 1998 2008 2018 2028 2038 2048 2058 2068 2078 2088
Figure 4 Total private assets
2500
2000
~O Z 1500
~0\
,...
; 1000
...
--=
- - - Wealth consumption ---- Baseline
500
O~~-r~~~-r~~-+~+-~-+~~
1988 1998 2008 2018 2028 2038 ~048 2058 2068 2078 2088
~
o
Z 1500
~0\
po4
S
1000.-
-- =
Figure 5 Foreign assets ineL petroleum wealth
2500 2000
500
_--/' ...
/' ...
/' ...
,
,, ,
...
...
- ....
_---o
~_+~~~~~+_~_+~+_~_+~~1988 1998 2008 2018 2028 2038 2048 2058 2068 2078 2088
---- Baseline
- - - Wealth consumption
petroleum wealth}. ~ng the years of tax reductions (1993-2013),increased private wealth counteracts the negative effects on the foreign asset position
stemming from declining public wealth as well as from the increased demand for residential investment. This explains why the negative effects of the wealth
consumption policy on foreign assets occur with a considerable time lag, compare Figure 2 and Figure 5.
Itis natural to ask how sensitive our conclusions are to changes in the interest rate, keeping the rates of time preference and long-run growth constant. To examine this question, the simulation experiments above were repeated with real interest rates equal to 2 and 7 percent respectively. The corresponding petroleum wealth estimates were revised to 1247 and 563 billion kroner. The 2 percent rate implies a lower permanent income from the government petroleum wealth than the 4
percent case, and therefore taxes are somewhat higher. Intertemporal substitution yields a flatter consumption profile over the life cycle, generating less private wealth than previously. Opposite conclusions follow when the rate of interest is 7 percent.
A lower interest rate reduces the cost of a wealth consumption policy because more generations gain and the reduction in steady state consumption is smaller.
This is illustrated in Figure 6 and 7, which show the consumption of successive generations when each are in age group 40-44 years for the 2 and 7 percent cases respectively, compare Figure 3. The eight first generations gain in the case of 2 percent interest rate, the six first generations gain in the 4 percent case and the five first generations gain if the rate of interest is 7 percent. In steady state consump-tion drops relative to baseline by approximately 7 percent in the 2 percent interest case, 14 percent in the 4 percent case and as much as 24 percent in the 7 percent case.
5. CONCLUSIONS
Due to the huge petroleum wealth owned by the Norwegian government, the choice of fiscal policy strategy for spending the petroleum revenues could have a
Figure 6 Changes in consumption per capita relative to baseline, age group 40-44 years - 2 percent interest rate
8,00%
-4,00%
4,000/0
-8,00%
1988 1998 2008 2018 2028 2038 2048 2058 2068 2078 2088
Figure 7 Changes in consumption per capita relative to baseline, age group 40-44 years - 7 percent interest rate
4,000/0
-4,00%
-8,00%
-12,00%
-16,00%
-20,00%
-24,00%
-28,00%
1988 1998 2008 2018 2028 2038 2048 2058 2068 2078 2088
significant impact on the welfare of future generations. To address this question, we used a computable overlapping generations model to simulate two different scenarios. The model captures the ageing of the population due to low fertility rates after 1970, and takes into account the effects of social security transfers and bequests on consumption and saving, assuming a "joy-of-giving" bequest motive.
Inthe first baseline scenario, the petroleum wealth is transformed into foreign assets before a steady state growth path is approached in the very long run. Inthis case all generations will benefit from the initial petroleum wealth. The second scenario assumes that the government's petroleum wealth is consumed over a period of 40 years, leaving future generations with a permanent lower stock of public wealth and higher taxes. The intergenerational welfare effects turn out to be substantial, particularly for the very young and all unborn generations. Insteady state, per capita consumption is 14 percent lower than in the baseline case, assum-ing a gap between the annual real rate of interest and the natural rate of growth of about 3.5 percentage points. The effects are somewhat sensitive to the size of this gap. ff the real rate of interest is 2 percent.-the reduction in steady state consump-tion (per capita) is 7 percent, and in the case of a 7 percent real rate of discount, the corresponding reduction in consumption is as large as 24 percent,
APPENDIX
The simulation model Production
Private output (excluding the housing sector) is generated by a constant returns to scale Cobb-Douglas production function:
Here X, is the contribution to GDP in period t, A,Lt is the effective labor supply, L, is labor supply measured in natural units,
K,
is capital and ais the constant labor share. L,grows with the rate n and A,with the rate A. The marginal product of capital is equal to the rental price, r+fI, where r is the constant real interest rate and flis the rate of depreciation of private real capital. Itfollows that the capital intensity ktæKJLt is determined by the rental price and the parameters of the production function:Since L, is given exogenously, the optimal
K,
is derived from (2), and gross investment is given by(3) It
=
Kt - Kt_1+ aPKt·The real product wage (wt) is equal to the marginal product of labor, i.e.
(4) W•t
=
aAUk1-at t •The government's demands for labor and physical capital are exogenous.
Household behavior
The model consists of 12 active overlapping generations. We assume that the four youngest and the four oldest generations are supported by their parents and the government respectively. The demographic development is given by age-specific fertility rates and age- and sex-specific mortality rates. The generations of age 20-40 become parents and for simplicity no one dies before the age 45.
Consider a representative grown-up individual entering the first period of bis life cycle (age 20-25) at the beginning of period t. His utility function is a time separa-ble CES function with an intertemporal elasticity of substitution equal to l/y,"(>O,
(5) U1,1
=
l-y1(
~u13
j)+j-l Cj,l+j-l1-, +13
13,1+12B1-,13,1+12r
, •Here Cj,l+j_l is consumption in age period j (j=1,...,12)at time t+j and B13,'+12 is
bequest to the offspring. The weights 13j,l+j-l are defined by (6)
where Nj,t+j_l is the number of adults in generation j in period t+j-l, NS,l+j-l is the number of children in age-group 5 (5=-3,-2,-1,0) in period t+j-l,
es
captures the expenditures related to the resposibility for children and pis the pure rate of time preference. The weight f3t3,1+12 iswhere 1') is a parameter reflecting the strength of the "joy-of-giving" bequest motive.
Total consumption is a CES composite good consisting of the consumption of housing services (h) and nondurable consumption (c). Assuming a constant rate of interest, the intertemporal budget constraint is given by
12
(8)
E
(l-r)j-lP'Cj,l+j_l + (1_r)12 B13,1+12 = Vu'j-l
where P is the constant price index of the composite good, r is the constant real after tax interest rate and V1" is the present value of allfuture after tax wage income, received bequest and social security transfers. Vu is defined as
(9)
12
VI'
=
r (l-rY-l(w .•. IL. •. 1 + TR .•. 1 + B.•. 1)·,. ~ J.. +J- J,.+J- J.. +J-
J,.+J-J-l
Here TRj,l+j_l is the social security contributions, W,+j_l is the real after tax wage rate,
Lj,t+j-1 is thelabor supply and Bj,t+j-1 is bequest received from previous generations.
Maximization of (5) subject to (8) gives standard demand functions for Cj,t+j-l and
B13,t+12' j=1, ...,12.The corresponding demands for nondurables and housing
con-sumption are
(10) C.,
"~-
.1=
(aC/P)" C,, .,~~-
l'and
(11) h.,fl
=
[al(r+a")/p]"C., . 1.,~+ -
1~+1-Here
a"
is the rate of depreciation for housing wealth, (J is the atemporal elasticity of substitution between Cand h, and aC and ah are the corresponding weights.National wealth
National wealth (excluding human capital) is given by:
(12) NW,
=
K, + Kg, +H, +F"where K',is the public capital stock, H, is private housing wealth, Ffis the sum of foreign assets and the exogenous petroleum wealth. Insteady state all the compo-nents in (16) are constant per efficiency unit of labor.
Calibration
The model is calibrated to the Norwegian economy mainly by using data from the National Accounts. Both private and government wealth and the foreign debt for 1988 are reproduced in the model's initial period. Some key parameter values are given in table A-l.
Calibration of the initial allocation of wealth between the generations gave a rate of time preference equal to 0.20 percent on an annual basis. The Tlparameter reflecting the bequest motive is calibrated such that the bequest in the model's initial period is equal to 1 percent of GDP in 1988 (Gjersem, 1992). Assuming a partial recovery of the fertility rate from the low level of the 19805, the long-run
population growth rate is -0.30. The 0.5 percent values of the intertemporal elasticity of substitution (l/y) and the atemporal elasticity of substitution of the consumption bundle (Cf) as well as the 0.66 percent rate of labor-augmenting technical progress are broadly consistent with existing empirical evidence. For more details about calibration and parameter values, see Steffensen and Steigum
(1990).
Real rate of interest Rate of time preference
Intertemporal elasticity of substitution (l/y) Atemporal elasticity of substitution (Cf)
Rate of technical progress (labor-augmenting) Long-run population growth rate
4 0.20 0.5 0.5 0.66 -0.30
(annual) (annual) (annual) (annual) Table A-l. Some key parameters, percent.
REFERENCES
ABEL, A.B. and M. WARSHAWSKY (1988): "Specification of the Joy of Giving:
Insights from Altruism", The Review
of
Economics and Statistics, 70, 145-149.ASLAKSEN, I., K.A. BREKKE, T.A. JOHNSEN and A. AAHEIM (1990): ''Petroleum resources and the management of national wealth", in O. Bjerkholt,
ø.
Olsen and J.VisUe (eds), Recent Modelling Approaches in Applied Energy Economics, Chapman and Hall, London.
AUERBACH, A.J. and L.J. KOTLIKOFF (1987):Dynamic Fiscal Policy, Cambridge University Press, Cambridge.
BARRO, RJ. (1974): "Are Government Bonds Net Wealth?", Journal
of
Political Economy,82,1095-1117.BLINDER, A.S. (1974):Towards an Economic Theory
of
Income Distribution, MIT Press, Cambridge, Mass.DIAMOND, P.A. (1965): ''National debt in a neoclassical growth model", American Economic Review, 55, 1126-1150.
GJERSEM, Carl E. (1992): "Arv og formue i en overlappende generasjonsmodell"
(Bequest and wealth in an overlapping generations model), SNF-Report no. 34/92, Foundation for Research in Economics and Business Administration, Norwegian School of Economics and Business Administration, Bergen. .
PERSSON, T.(1985): "Deficits and intergenerational welfare in open economies", Journal
of
International Economics, 19, 67-84.STEFFENSEN, E. and E. STEIGUM, Jr. (1990): "Overmod: En numerisk overlappen-de generasjonsmooverlappen-dell for norsk økonomi - Et dokumentasjonsnotat" (Overmod: A numerical overlapping generations model of the Norwegian economy), Working Paper no. 57/90, Foundation for Research in Economics and Business Adminis-tration, Norwegian School of Economics and Business Administration, Bergen.
STEIGUM, [r., E. (1993): "Accounting for long run effects of fiscal policy by means of computable overlapping generations models", in S. Honkapohja and M. Ingberg (eds), Macroeconomic Modelling and Policy Implications, Elsevier Scienæ Publishers B.V., Amsterdam.
THØGERSEN,